In an interview Sunday, Anthony Fauci, head of infectious diseases at the National Institutes of Health, said that a "rolling" reopening of the economy might be possible as soon as May -- in some parts of the country -- as the pandemic comes under control and antibody testing becomes widely available. How that rollout might affect you and your business will depend on where you are and what you do.

In a conversation with CNN's Jake Tapper, Fauci explained what such a rolling reopening might look like and where it might begin, along with some caveats. Here are his main points.

1. It won't be like flipping a switch.

"It is not going to be a light switch that we say, 'It is now June or July or whatever. Click! the light switch goes back on,' " Fauci explained. "It's going to be depending where you are in the country, the nature of the outbreak that you've already experienced and the threat of an outbreak that you may not have experienced."

Obviously, he said, the situation in places like New York City or New Orleans is very different from in places such as Arkansas, or on the West Coast, where Washington State has successfully prevented a big spike in new cases. "It's going to have to be something that is not one-size-fits-all," he said.

As to when it might begin, he said, "We are hoping that at the end of the month we can look around and say, 'OK, is there any element here that we can safely and cautiously start pulling back on?' If so, do it. If not, then just continue to hunker down."

He made two disclaimers, though. First, he said, "It's so difficult to make those kinds of predictions because they always get thrown back at you if it doesn't happen." And second, when and how to reopen the economy is not up to him or any other doctor. "Decisions are going to have to be made at the level of the president and the governors."

2. Inevitably, some people will get sick.

It's obvious that the economy can't stay in its current locked-down state forever. But when restrictions begin to be relaxed, "We know there will be people who will be getting infected. That is just reality," Fauci said. 

Given that reality, "The critical issue is to be able to, in real time, identify, isolate, and contact trace. That's containment." It's too soon, though, for some locations to be considering containment, he noted. "Right now, in places like New Orleans and New York City, we're in mitigation."

3. Widespread antibody testing will make all the difference. 

Medical professionals in many parts of the country have raised concerns about the availability of tests for coronavirus infection. Those tests are essential for treating patients with flu-like symptoms, which could be Covid-19, or possibly something else. Fauci stressed that this type of testing needs to continue in order to evaluate and treat people who may be infected with Covid-19.

But getting the nation back to work requires a different type of test, one that looks for antibodies to the virus and is typically administered to healthy people. Many who are infected with the coronavirus have only mild symptoms or none at all, so widespread antibody testing will tell us how deeply the virus has penetrated our society.

That's important information, Fauci says. He suspects that a large number of Americans have already been infected with the coronavirus but don't know it because they never got very sick. For people who've already been infected, he said in a different interview, "one could formulate strategies about whether or not they'd be at risk." And, Fauci says, widespread antibody testing will be available very soon, perhaps within days in some parts of the country.

Fauci also praised the many governors he's spoken with over the past several days. "I'm deeply impressed about how much they care about the balance of preserving the health of the citizens in their states at the same time as they cautiously do this reentry," he said. "So I have confidence with the help that we can do from the federal government and the fact that the states are really committed to doing it right, I think that combination hopefully is going to get us where we want to be."